1. Field of the Invention
This invention relates generally to the flight control of an aircraft and, more particularly, to providing a smooth transition of an aircraft between aircraft flight operating in response to the calculated airspeed value and aircraft flight operating in response to the Mach number value.
2. Description of the Related Art
In the modern aircraft, low altitude control of an aircraft is performed in relationship to the calibrated airspeed (CAS) of the aircraft, while the high altitude control of aircraft is performed in relationship to the Mach number. When climbing to or descending from a high cruising altitude, it is necessary for the control apparatus of the aircraft to make the transition between response to the calibrated airspeed and the Mach number. Generally, a calibrated airspeed parameter or Mach number parameter is preselected by the flight deck of the aircraft, the preselected parameter being the parameter value for the aircraft after the transition. In the alternative, the flight deck of an aircraft can select an altitude (typically 26,000 feet) at which the transition is to take place.
However the transition of the control between the calibrated airspeed value and the Mach number value can involve overshoot of the preselected target aircraft speed. The calibrated airspeed and the Mach number are related by the true airspeed (TAS). When the aircraft is changing altitude while holding a selected calibrated air speed, the expression to convert the calibrated airspeed to the true airspeed is given by the expression: EQU TAS={7.times.G.times.R.times.T[{(P.sub.o /P)[{1+0.2(CAS/C.sub.o).sup.2 }.sup.3.5 -1]+1}.sup.(2/7) -1]}.sup.1/2 1.
where:
T=ambient temperature (.sup.o K) PA1 P.sub.o =sea level air pressure (2116.2 lb/ft.sup.2) PA1 C.sub.o =sea level speed of sound (661.45 knots) PA1 R=ideal gas constant (96.03 ft/.sup.o K) PA1 G=sea level acceleration of gravity (32.174 ft/sec.sup.2) PA1 P=static pressure (lb/ft.sup.2)
From the foregoing equation, the true air speed increases as temperature increases and decreases as pressure increases. However, the changes in pressure are more important during a change in altitude. The result is a positive acceleration along the flight path during a climb and a negative acceleration during descent in the flight path, i.e., when the specific calibrated airspeed is maintained.
The corresponding expression for true airspeed in terms of the Mach number is: EQU TAS=(1.4.times.G.times.R.times.T).sup.1/2 (Mach number) 2.
where G, R, and T have been previously defined.
Referring to equation 2, when the Mach number is held constant, the true air speed increases with temperature. Because the temperature decreases with increasing altitude in the troposphere, a negative flight path acceleration results for the true air speed during an increase in altitude and positive flight path acceleration occurs for the true air speed during a negative change in altitude when the Mach number is held constant. (The derivation of the true air speed equations 1 and 2 can be found in Airplane Aerodynamics and Performance, Tau Edward Lan and Jan Roskam, Roskam Aviation, 1980, pages 15-25).
Because of the acceleration (positive or negative) of the true airspeed for a change in altitude, when the transition between the constant calibrated airspeed and the constant Mach number occurs, an overshoot in the target control parameter (i.e., the calibrated air speed or the Mach number) is experienced with the corresponding requirement to adjust the control parameter to the selected value.
In the prior art, transfer was made to the alternative parameter when the calibrated airspeed or the Mach number reached the preselected value of the alternate parameter. The preselected value of the alternative parameter was subject to overshoot, causing the aircraft to reverse the acceleration after transfer to the alternative parameter.
A need has therefore been felt for apparatus and an associated method to provide smooth transition from an aircraft operating in response to a constant calibrated airspeed parameter to a constant Mach number parameter or to provide a smooth transition when the control parameter of the aircraft changes from the calibrated airspeed to the Mach number at a preselected altitude.